Archimedes' dimension of the circle: A view of the genesis of the extant text

  title={Archimedes' dimension of the circle: A view of the genesis of the extant text},
  author={Wilbur Richard Knorr},
  journal={Archive for History of Exact Sciences},
  • W. Knorr
  • Published 1 December 1986
  • Physics
  • Archive for History of Exact Sciences
Of all the works in the Archimedean corpus, none has been more widely studied from ancient and medieval times to the present day than the short tract on the measurement of the circle. It was cited frequently by the ancient mathematical commentators, was known in the Latin Middle Ages in translations both from the Arabic and directly from the Greek, and remains prominent in all general discussions of Archimedes' geometry to this day.1 The popularity of this work is easily understood. Its… 
22 Citations
Architecture and Mathematics in Ancient Egypt: The proportions of pyramids
Analysing true pyramids Numerological theories It is virtually impossible to mention all of the theories that have been suggested to explain the geometry of Egyptian pyramids. Many of them are based
Architecture and Mathematics in Ancient Egypt: Documents on the planning and building process
Architectural drawings Representations of buildings and working drawings Representations of buildings are frequently found in Egyptian art, and in many cases they provide a large amount of
Circular reasoning: who first proved that $C/d$ is a constant?
We answer the question: who first proved that $C/d$ is a constant? We argue that Archimedes proved that the ratio of the circumference of a circle to its diameter is a constant independent of the
Architecture and mathematics in ancient Egypt
Part I. Proportions in Ancient Egyptian Architecture: 1. In search of 'the rule' for Ancient Egyptian Architecture 2. Mathematics and architecture in Ancient Egypt Part II. Ancient Egyptian Sources:
Circular Reasoning: Who First Proved That C Divided by d Is a Constant?
Summary We argue that Archimedes proved that the ratio of the circumference of a circle to its diameter is a constant independent of the circle and that the circumference constant equals the area


Archimedes and the elements: Proposal for a revised chronological ordering of the Archimedean corpus
The present reexamination of this question of Archimedean chronology will show how tenuous are the foundations of the orderings now in standard usage, and present a chronological order which differs from the standard accepted sequence in certain important respects.
The Hyperbola‐Construction in the Conics, Book II: Ancient Variations on a Theorem of Apollonius
In the fourth proposition of Book II of Apollonius' Conies one finds a method of constructing the hyperbola of which a point and both asymptotes are given. But a close examination of this proposition
Archimedes and the measurement of the circle: A new interpretation
In the third propos i t ion of the Dimensio Circuti, ARCHIMEDES established 3-~ as an upper bound , 3~7~ ° as a lower b o u n d for the ra t io of the perimeter to the diameter of the circle.
The Mathematician Zenodorus
Z ENODORUS the mathematician is best known for his treatise n€p' lC01T€PLf.LhpWll1 cX1Jf.La:rwll, On Figures of Equal Boundary. This, like all his works, is lost, but part of its contents has been
Archimedes'On the Measurement of a Circle Proposition 1: An Attempt at Reconstruction
Les versions du texte d'Archimede sur la mesure du cercle, dans l'Antiquite et le Moyen-Age. Pappus, Theon d'Alexandrie, Gerard de Cremone, Plato de Tivoli, Al Tusi, J. L. Heiberg.
A history of Greek mathematics
A text which looks at the history of Greek mathematics - a subject on which the author established a special authority by his succession of works on Diophantus, Apolonius of Perga, Archimedes, Euclid
Thirteen Books of Euclid's Elements
There is disclosed a telephone number indexing device which comprises a casing having an upper opening and housing therein a plurality of cards on which telephone numbers are recorded. When any card
On Burning Mirrors